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# Notes section 4.7

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Notes for Section 4.7 - Geometry

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### Notes section 4.7

1. 1. Section 4.7 Use Isosceles and Equilateral Triangles
2. 2. THEOREM 4.7: BASE ANGLES THEOREM If two sides of a triangle are congruent, then the angles opposite them are congruent. If AB  AC, then B  C
3. 3. THEOREM 4.8: CONVERSE OF BASE ANGLES THEOREM If two angles of a triangle are congruent, then the sides opposite them are congruent. If B  C, then AB  AC.
4. 4. Example 1 Find the unknown measure.
5. 5. Example 2: Find the value of x.
6. 6. Example 3: Find the values of x and y.
7. 7. Example 4: Find the perimeter of the triangle.
8. 8. Example 5: Garden You plant a garden in the shape of a triangle as shown in the figure. What is the perimeter
9. 9. Find the measures of R,  S, and  T.
10. 10. Unit 5.1 - Notes midsegment_ – a segment that connects the midpoint of two sides of a triangle. So LM, MN, and LN are the midsegments of triangle ABC.
11. 11. Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
12. 12. EX 1: If QR = 18, then JK is half of it which means JK = 9. If PK = 8, then KR = 8 since K is the midpoint of PR. Since PR = 16 all together, JL is half of PR since it is between the two midpoints so JL = 8. If KL = 6, then PQ is double KL so PQ = 12. KR = 8, LR = 9, QL = 9, PJ = 6, JQ = 6 Perimeter of PQR = 18 + 12 + 16 = 46 Perimeter of JKL = 6 + 8 + 9 = 23
13. 13. EX 2: Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex. a) a square with sides of length m b) an acute triangle with base length b
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